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arXiv · 2108.01325

The signless Laplacian state transfer in Q-graph

Xiao-Qin Zhang·Shu-Yu Cui·Gui-Xian Tian
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Abstract

The $\mathcal{Q}$-graph of a graph $G$, denoted by $\mathcal{Q}(G)$, is the graph derived from $G$ by plugging a new vertex to each edge of $G$ and adding a new edge between two new vertices which lie on adjacent edges of $G$. In this paper, we consider to study the existence of the signless Laplacian perfect state transfer and signless Laplacian pretty good state transfer in $\mathcal{Q}$-graphs of graphs. We show that, if all the signless Laplacian eigenvalues of a regular graph $G$ are integers, then the $\mathcal{Q}$-graph of $G$ has no signless Laplacian perfect state transfer. We also give a sufficient condition that the $\mathcal{Q}$-graph of a regular graph has signless Laplacian pretty good state transfer when $G$ has signless Laplacian perfect state transfer between two specific vertices.

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Xiao-Qin Zhang, Shu-Yu Cui, Gui-Xian Tian. 2021-08-03. The signless Laplacian state transfer in Q-graph. https://arxiv.org/abs/2108.01325

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